AN EFFECTIVE AND SIMPLE SCHEME FOR SOLVING NONLINEAR FREDHOLM INTEGRAL EQUATIONS

In this paper, a simple scheme is constructed for finding approximate solution of the nonlinear Fredholm integral equation second kind. To end, Lagrange interpolation polynomials together with Gauss-Legendre quadrature rule are used to transform source problem system algebraic equations. Afterwards, resulting can be solved by Newton method. The basic idea choose points same as integration. This facilitates evaluation part equation. We prove that converges uniformly exact solution. Also, stability investigated. advantages method simplicity, fastness and accuracy which enhance its applicability in practical situations. Finally, we provide some test examples.